A car rental company offers two plans for renting a car: Plan A, which costs $30 per day and an additional 13 cents per mile, and Plan B, which costs $50 per day with free unlimited mileage.
To determine the range of miles for which Plan B will save you money for a 1-day rental, we need to find the point at which the cost of Plan A exceeds the cost of Plan B.
Let's assume the number of miles driven in a day is represented by "m".
For Plan A, the cost can be calculated as follows:
Cost of Plan A = $30 (daily rate) + $0.13 (cost per mile) * m (number of miles driven)
For Plan B, the cost is a flat rate of $50 per day, regardless of the number of miles driven.
To find the range of miles for which Plan B is cheaper, we need to set up an inequality:
Cost of Plan A > Cost of Plan B
$30 + $0.13m > $50
To solve this inequality, we can subtract $30 from both sides:
$0.13m > $20
Next, we divide both sides by $0.13 to isolate "m":
m > $20 / $0.13
m > 153.85
Therefore, to save money with Plan B, the number of miles driven in a day must be greater than 153.85 miles.
Answer: The mileage must be greater than 153.9 miles per day.